1. The child's height after age 6 is a linear function of his age because it grows at a constant rate annually.
2. The child's growth rate is 5% with an initial value of 40 inches.
3. A linear function that represents the scenario is , H(t) = 40 + 2t.
What is a linear function?A linear function is a mathematical expression with variables multiplied by constants appearing in the first degree.
The mathematical operations involved in a linear function are addition and subtraction.
A linear function represents a straight line on the coordinate plane.
Data and Calculations:Initial height at age 6 = 40 inches
The annual growth rate in inches = 2 inches
Growth rate in percentage = 5% (2/40 x 100)
Linear Function for H:H(t) = 40 + 2t
Where t = years after age 6
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Question Completion:Using t for the time in years since age 6 and H for height in inches, find a formula for H as a linear function of t.
The midpoint of \overline{\text{AB}} AB is M(7, 0)M(7,0). If the coordinates of AA are (8, -3)(8,−3), what are the coordinates of BB?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{8}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +8}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(7~~,~~0)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +8}{2}=7\implies x+8=14\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3}{2}=0\implies y-3=0\implies \boxed{y=3}[/tex]
Define sets U, A, B, and C as shown below. Find A'n (BUC').
U= ({a,b,c,d,e,f.g.h}
A = {f,g,h}
B={a,g,h}
C={a,b,c,d,e)
Answer:
{a}
Step-by-step explanation:
You want the set A'∩(B∪C') given the definitions of each of the sets U, A, B, C.
Inverse setsThe inverse of a set is the set of elements of the universal set that are NOT in the given set.
A' = {a, b, c, d, e, f, g, h} - {f, g, h} = {a, b, c, d, e}
C' = {a, b, c, d, e, f, g, h} - {a, b, c, d, e} = {f, g, h}
UnionThe union of two sets is the list of elements in either of the two sets.
B∪C' = {a, g, h} +{f, g, h} = {a, f, g, h}
IntersectionThe intersection of two sets is the list of elements common to both:
A'∩(B∪C') = {a, b, c, d, e} ∩ {a, f, g, h} = {a}
In a warehouse, there are 2 robots that work together. They move in the same direction concurrently, so if one moves North, they both North. The robots will follow any instructions they’re given and will collect any objects they find along the way. They only take instructions by the points of the compass and can only move in 4 directions (N, E, S, W).
For example, if the 2 robots are given the directions: “N, E, S”, then Robot A will collect a ball and Robot B will collect a hat.
Write the directions the robots would need to follow to collect the following objects, remembering that both robots get the same directions, and assuming that for each question they start off in the same (pictured above) positions:
1. Robot A: ball Robot B: ball
2. Robot A: hat, ball Robot B: box, hat
3. Robot A: ball, ball Robot B: hat, ball
1. For collecting balls by both Robot A and B the direction will be N->E->E
2. For collecting hat and ball by Robot A and box and hat by Robot B, the direction will be N->N->S->E->E
3. For collecting both the balls by Robot A and a hat and ball by Robot B, the direction will be E->E->N
The direction that both Robot A and Robot B can take are N, E, S and W
For Part 1:
Robot A and Robot B need to collect the ball which is in the 2nd row 5th column for Robot A and 4th row 3rd column for Robot B, therefore the direction will be:
=N->E->E
For Part 2:
Robot A needs to collect a hat and ball which are in the 1st-row third column and 2nd row 5th column respectively. Robot B needs to collect a box and a hat which are in the 3rd row 1st column and 4th row 3rd column respectively. Therefore, the direction will be:
= N->N->S->E->E
For Part 3:
Robot A needs to collect both the balls which are in the 3rd-row 4th column and 2nd row 5th column respectively. Robot B needs to collect a hat and a ball which are in the 5th row and 2nd column & 4th row 3rd column respectively. Therefore, the directions will be:
= E->E->N
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Which of the following mass values is equal to 40,000 grams?
A. 40 kilograms
OB. 40 milligrams
OC. 4 kilograms
OD. 4,000 megagrams
Answer:
A
Step-by-step explanation:
1 kilogram is equal to 1000 grams, so 40000 grams is 40 kilos.
IM GIVING BRAINLIEST! PLEASE I NEED HELP! Ava had $28.50 to spend at the farmer's market. After buying 3 pumpkins Ava, has $12 left. Which equation could you use to find the price of one pumpkin (x)?
28.50/3=x
3x-12=28.50
x+12=28.50
3x+12=28.50
on the same axes draw the graphs of y=2x and y=2xt5(tables for y=2x and y=2xt5)
The graph for y=2x and y=2x + 5 is drawn at bottom.
Why are graphs used by mathematicians?A common technique for graphically showing data linkages is the graph. While taking up less space, a graph accomplishes the goal of conveying information that are either too many or complicated to be completely stated in the text.
A graph is a diagram or graphical representation that organizes the display of facts or values. The points on a graph are typically used to depict the relationships between two or more things.
For the given question,
y = 2x
The coordinates are -
(1,2), (2,4), (3,6), (4,8)
y=2x + 5
The coordinates are -
(1,7), (2,9), (3,11), (4,13)
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Monica sold 3 pairs of her old Slick Sprinter sneakers at the Re-Laced secondhand store. Before she left, Monica spent $13 of her earnings on a used pair of boots. She had $8 remaining. How much did Monica receive for each pair of sneakers?
Monica received $ 7 amount of money for each pair of sneakers she sold.
We are given that:
Remaining amount with Monica = $ 8
She spent on earing = $ 13
The total amount she had = $ 13 + $ 8
The total amount she had = $ 21
Now, she sold 3 pairs of sneakers and gained $ 21
So, the price of each snicker will be calculated by using division.
So, we get that:
Monica receive for each pair of sneakers = $ 21 / 3 = $ 7
Therefore, Monica received $ 7 amount of money for each pair of sneakers she sold.
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The volume of a right rectangular prism is found by multiplying the length of the base by the width of the base by the height of the prism. A right rectangular prism has a volume of 30 cubic inches. If the height of the prism is 6i inches, what is the area of the base of the prism?
If the height and volume of the prism are 6 inches and 30 cubic inches. Then the base area of the prism is 5 square inches.
What is a rectangular prism?
A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.
The volume of a right rectangular prism is found by multiplying the length of the base by the width of the base by the height of the prism.
A right rectangular prism has a volume of 30 cubic inches.
If the height of the prism is 6 inches. Then the base area of the prism will be
The volume is given as
Volume = Base area × Height
We know
Volume = 30
Height = 6
Then the base area will be
30 = Area × 6
Area = 5
Given h(x) = 5x-1, find h(-4)
Step-by-step explanation:
h(-4) = 5(-4) - 1
= -20 - 1
= -21.
Answer:
-21 is correct
Step-by-step explanation:
Dana has driven her car 95,598 miles. She estimates she can
drive the car another 5000 miles before the mileage reaches
100,000 miles. Use the rules for estimating differences to
explain if Dana is correct.
Answer: Dana estimation is incorrect because difference = 598 miles
Step-by-step explanation:
Given data,
Dana has driven her car 95,598 miles.
She estimates she can
drive the car another 5000 miles.
she can,
drive the car another 5000 miles before the mileage reaches
100,000 miles.
Estimated Mileage of the car is equal to 100,000 miles.
That is,
Estimated Mileage of the car is = 100,000 miles.
So,
We can write,
Total distance Dana has to travel = already driven + additional miles to cover
Total distance Dana has to travel = 95,598 + 5,000 miles
Total distance Dana has to travel = 1,00,598 miles.
As per mileage of car is 100,000 miles.
So, Dana has to travel = 1,00,598 miles.
So, Dana estimation is incorrect because difference is = 100,598 - 100,000
Therefore,
Dana estimation is incorrect because difference = 598 miles
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Find the midpoint of a line segment with endpoints at left parenthesis 1 comma space 7 right parenthesis and left parenthesis 9 comma space minus 3 right parenthesis.
The midpoint of the line segment with endpoints at (1, 7) and (9, -3) is (5, 2)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The midpoint O(x, y) of the line segment with endpoint at A(x₁, y₁) and B(x₂, y₂) is:
x = (x₁ + x₂) / 2; y = (y₁ + y₂)/2
Given the line segment with endpoints at (1, 7) and (9, -3). Let O(x, y) be the midpoint, hence:
x = (1 + 9) / 2 = 5
y = (7 + (-3)) / 2 = 2
The midpoint of the line segment with endpoints at (1, 7) and (9, -3) is (5, 2)
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Jane has a pre-paid cell phone with Splint. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 320 minutes and the cost was $143.00. In July she used 710 minutes and the cost was $279.50.
The cost function expressed as the number of times spent calling is cost function = c(x) = 31 + 0.35x
How to solve for the cost functionThe cost function that can be written as per the number of units that she used is given as
c(x) = a + bx
x = 320
a + 320b = 143
When x = 710
we would have
a + 710b = 279
subtract the equations
710 b - 320 b = 279 - 143
390b = 136
b = 136/390
= 0.35
Put the value of b in equation 1
a + 320 x 0.35 = 143
a + 112 = 143
a = 31
cost function =
c(x) = 31 + 0.35x
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complete questionA) Express the monthly cost C as a function of a, the number of minutes of calling time she used.
Adam invests 16,000 in an investment certificate (GIC) that pays 3 percent, compounded annually.
How much interest will he have earned after two years?
$867.40
$960.00
$974.40
$1,031.40
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}[/tex]
[tex]A=16000\left(1+\frac{0.03}{1}\right)^{1\cdot 2} \implies A = 16974.4~\hfill \underset{earned~interest}{\stackrel{16974.4~~ - ~~16000}{ 974.40}}[/tex]
Please help ASAP
Which Venn diagram has shading that represents the given set?
[tex]S^{C}[/tex] ∩ T sets is the option C.
How to represent sets in Venn diagram?Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
A set is a collection of items.
S is a set and T is also a set.
[tex]S^{C}[/tex] simply means S complement.
Complement of S simply means not in S. It means everything not in S.
∩ simply means intersection
Therefore,
[tex]S^{C}[/tex] ∩ T implies not in S intersection T sets.
Hence, [tex]S^{C}[/tex] ∩ T is the option C.
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Area de una pared 42 ²/3 yardas cuadradas Angela usa 1 galon y 1/3 de pintura. i Cuál es la tasa de cobertura de Angela en yardas cuadradas por galón y 1/3 de pintura?
Responder:
Parte A: 32 yardas cuadradas por galón
Parte B: 13 pies cuadrados por galón de diferencia
Explicación paso a paso:
Parte A:
Para saber cuántas yardas cuadradas cubre cada galón, tienes que dividir 42 2/3 entre 1 1/3, lo que equivale a 32. Eso significa que cada galón de pintura cubre 32 yardas cuadradas.
Parte B:
Primero, tienes que convertir cuánto cubrió Ángela en yardas cuadradas a pies cuadrados. Como una yarda cuadrada equivale a 9 pies cuadrados, tenemos que multiplicar 32 por 9, lo que equivale a 288. Para encontrar la diferencia, debes restar 288 - 275, lo que equivale a 13.
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Your cousin renews his apartment lease and pays a new monthly rent his new rent is a calculated by applying a discount of $50 to his original rent and then applying at 10% increase to the discounted amount what was your cousins original monthly rent when his new rent is 5% greater
Answer:
10000000$
Step-by-step explanation:
gu kha le bhosadike duck you
Write a ratio that forms a proportion with 2/9
The ratio that forms a proportion with 2/9 in the question is 14/63.
What is ratio?
Ratio can be described as the term that is been used in mathematics which is been used in the indication of how many times one number contains another.
From the given figure, which is 2/9 , the ratio that form the proportion can be found as
[(2*7) / (9*7) ]= 14/63
In conclusion we can see that the ratio that forms a proportion with 2/9 in the question is 14/63 because if we follow the way the ratio is been calculated , we can see that 14/63is the correct answer, which is option D.
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The missing options are:
10/40
12/63
12/45
14/63
need help math worklkkk
The table of values shows the output values of three different equations for the same input values, x.
Drag the correct expression to each row to complete each equation.
An equation is a formula that expresses the equality of two expressions, by connecting them with the equal sign. The relations are: x+3, 3x², 3ˣ
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equal sign.
Finding the relations:
Relationship 1:
The y-values have a common difference of 1, so the relationship is linear with as slope of 1. The only matching choice is (x+3), which matches the values of y1.
Relationship 2:
The y-values have differences that increase with a common difference. They are (3-0) = 3, (12-3) = 9, (27-12) = 15, (48 -27) = 21. The second differences are (9-3) = 6, (15-9) = 6, and so on with all second differences being 6. This tells you that a second-degree polynomial can model this sequence. The only matching choice is 3x² which matches the values of y².
Relationship 3:
The y-values have increasing differences that also have increasing differences. The values have a common ratio of 3, indicating an exponential function will model this sequence. The only matching choice is (3ˣ), which matches the values of y³.
Therefore the relations are: x+3, 3x² and 3ˣ
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Answer: Hope you guys can see it
Step-by-step explanation:
Eula needs to buy binders that cost $4 each and notebooks that cost $2 each. She has $20. The graph of the inequality 4x + 2y ≤ 20, which represents the situation, is shown. What is the greatest number of binders Eula can buy? What is the greatest number of notebooks Eula can buy? If Eula buys 7 notebooks, what is the greatest number of binders she can buy?
The required answers are,
The greatest number of binders Eula can buy is 5.
The greatest number of notebooks Eula can buy is 10.
If 7 notebooks are ordered, one binder may also be bought, costing $2 more for Eula.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now the given inequality is,
4x + 2y ≤ 20
here x is the number of binders and y is number of notebooks.
Cost of 1 binder = $4
Cost of 1 notebook = $2
Now for maximum number of binders put y = 0 in the given inequality we get,
4x + 2*0 ≤ 20
Solving we get,
4x ≤ 20
Dividing both the side by 4 we get,
x ≤ 5
Thus, Eula is permitted to acquire 5 binders in the absence of notebook purchases.
Now for maximum number of notebooks,
Putting x = 0 in the given inequality we get,
4*0 + 2y ≤ 20
Solving we get,
2y ≤ 20
Dividing both the side by 2 we get,
y ≤ 10
Thus, Eula is permitted to purchase 10 notebooks if no binders are purchased.
Now if Eula buys 7 notebooks, putting y = 7 in the given inequality we get,
4x + 2*7 ≤ 20
Solving we get,
4x + 14 ≤ 20
Subtracting both the side by 14 we get,
4x ≤ 6
Dividing both the side by 4 we get,
x ≤ 3/2
⇒ x ≤ 1.5 ≈ 2
Thus, If 7 notebooks are ordered, one binder may also be bought, costing $2 more for Eula.
Hence,If 7 notebooks are ordered, one binder may also be bought, costing $2 more for Eula.
Thus, the required answers are,
The greatest number of binders Eula can buy is 5.
The greatest number of notebooks Eula can buy is 10.
If 7 notebooks are ordered, one binder may also be bought, costing $2 more for Eula.
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Answer: 1) 5 2)10 3) 1
Step-by-step explanation:
on edge its correct
she sold 12 cupcakes for 42 dollars what is the constant of proportionality
The median number of pools installed by 9 construction teams in a certain summer is 11. The
range of the number of pools installed by those teams that summer is 14.
Determine if the following statement is true, is false, or does not contain enough information.
At least one team installed 11 pools
Answer: False. If this were true, then the range would have been 18 - 6 = 12.
Step-by-step explanation:
Evan has an even number of shells he has more than 10 shells and less than 15
Answer:
It can ither be 12 or 14
Step-by-step explanation:
The numbers have to be even and must be greater than 10 but less than 15 and the only numbers that are greater than 10 but less than 15 are 12 and 14.
Hope this helps.
a +x = b
solve for x?
Help me solve this I’ll give u vbucks
Answer:
49
Step-by-step explanation:
You first simplify (1/7)^2 which is 7^2 then you get 49.
Answer:
49
Step-by-step explanation:
did it
Plot the ordered pair -5,3
1/2
A graph of the given ordered pair (-5 3 1/2) has been plotted as shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is an ordered pair?An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.
In conclusion, the point (-5) would be plotted on the x-axis (abscissa) while point (3 1/2) would be plotted on the y-axis (ordinate) of a coordinate plane as shown in the image attached below.
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Need helpppp!!!!!!!!!!
Answer:
When x approaches -∞, y approaches ∞ and when x approaches ∞, y approaches ∞.
Step-by-step explanation:
How do you solve absolute value inequalities on both sides
Aleka and Helene both opened savings accounts that earn 2.5% interest a year. Aleka puts $2,500 into her account. Helene put $1,500 into her account and also saves $200 cash a year.
x = number of years
Aleka: f(x) = 2500(1.025)x
Helene: g(x) = 1500(1.025)x + 200x
Which function represents the difference, h(x) = f(x) – g(x), between the value of Aleka’s and Helene’s total savings after x years?
h(x) = –1000(1.025)x + 200x
h(x) = 1000(1.025)x + 200x
h(x) = 1000(1.025)x – 200x
h(x) = 4000(1.025)x + 200x
The function that represents the difference, h(x) = f(x) – g(x), between the value of Aleka’s and Helene’s total savings after x years is C. h(x) = 1000(1.025)x – 200x.
How to illustrate the function?It should be noted that Aleka and Helene both opened savings accounts that earn 2.5% interest a year. Aleka puts $2,500 into her account.
The function for Aleka will be:
= 2500 (1.025)^x
The function for Helene will be:
= 1500(1./25)^x + 200x
Therefore, the difference of the function will be 1000(1.025)x – 200x.
In conclusion, the correct option is C.
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Cm^2-g/cm^4
Does cm become cm^2. How to I subtract it?
Answer:
[tex]\frac{cm^{6} - g}{cm^{4} }[/tex]
Step-by-step explanation:
Write 1/cm^2 - g/cm^4 to visualize it better, then distribute using the fraction rule ([tex]\:a-\frac{b}{c}=\frac{ac-b}{c}[/tex]): [tex]\frac{cm^2cm^4-g}{cm^4}[/tex]
Combine like terms to get: [tex]\frac{cm^6-g}{cm^4}[/tex]
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